Animated Solution for Physics - Semiconductors: Which of the following gives a reversible operation?

Imagine a computer that generates absolutely zero heat. Sounds like science fiction? It is actually a concept rooted deeply in the physics of information, specifically Landauer's Principle. Today, we are going to explore the foundation of this idea by identifying a reversible operation among standard logic gates.

In computing and physics, an operation is considered reversible if you can perfectly deduce the input state just by looking at the output state. This requires a strict one-to-one mapping (a bijection) between inputs and outputs. If multiple different inputs can result in the exact same output, information is irrevocably lost. According to Landauer's Principle, the erasure of information is what fundamentally causes a logic gate to dissipate heat!

Let's look at the usual suspects: the OR, NOR, and NAND gates. These are standard $2$-input gates. Think about an OR gate. If I tell you the output is $1$, can you tell me what the inputs were?

They could have been $(0,1)$, $(1,0)$, or $(1,1)$. Because multiple input states lead to the exact same output, information is lost. You cannot reverse the process to find the original inputs. Therefore, any standard $2$-input to $1$-output gate is inherently irreversible.

Now, let's turn our attention to the fourth option. It is a NOR gate, but with a clever twist: both of its inputs are tied together to a single line, let's call it $X$. What happens here?

If $X=0$, both inputs are $0$, and the NOR gate outputs a $1$. If $X=1$, both inputs are $1$, and the NOR gate outputs a $0$. This configuration perfectly mimics a NOT gate.

A NOT gate simply flips the bit. If the output is $1$, you know with absolute $100\%$ certainty that the input was $0$. If the output is $0$, the input had to be $1$. There is no ambiguity. No information is lost.

This perfect one-to-one mapping is the hallmark of a reversible operation. By simply tying the inputs of a NOR gate together, we have created a reversible logic element!